Theorem fneq1i 5290

Description: Equality inference for function predicate with domain. (Contributed by Paul Chapman, 22-Jun-2011.)

Hypothesis

Ref	Expression
fneq1i.1	|- F = G

Assertion

Ref	Expression
fneq1i	|- ( F Fn A <-> G Fn A )

Proof of Theorem fneq1i

Step	Hyp	Ref	Expression
1		fneq1i.1	. 2 |- F = G
2		fneq1 5284	. 2 |- ( F = G -> ( F Fn A <-> G Fn A ) )
3	1, 2	ax-mp 5	1 |- ( F Fn A <-> G Fn A )

Syntax hints:   <-> wb 104   = wceq 1348   Fn wfn 5191

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-io 704  ax-5 1440  ax-7 1441  ax-gen 1442  ax-ie1 1486  ax-ie2 1487  ax-8 1497  ax-10 1498  ax-11 1499  ax-i12 1500  ax-bndl 1502  ax-4 1503  ax-17 1519  ax-i9 1523  ax-ial 1527  ax-i5r 1528  ax-ext 2152

This theorem depends on definitions:  df-bi 116  df-3an 975  df-tru 1351  df-nf 1454  df-sb 1756  df-clab 2157  df-cleq 2163  df-clel 2166  df-nfc 2301  df-v 2732  df-un 3125  df-in 3127  df-ss 3134  df-sn 3587  df-pr 3588  df-op 3590  df-br 3988  df-opab 4049  df-rel 4616  df-cnv 4617  df-co 4618  df-dm 4619  df-fun 5198  df-fn 5199

This theorem is referenced by:  fnunsn  5303  fnopabg  5319  f1oun  5460  f1oi  5478  f1osn  5480  ovid  5967  tfri1d  6312  frec2uzrand  10354  frec2uzf1od  10355  frecfzennn  10375  dfrelog  13540  nninfsellemeqinf  14014